Sorry for your loss, I went through the same recently.  Now my run is covered with heavy duty netting as a deterrent.  Live and learn, I suppose.
Your run needs to be far more secure.  Chicken wire, plastic sheet and netting, none of those things are predator resistant and I fear what might happen if a dog, coyote, raccoon, etc. were to come around.  If you and your family aren't really handy and want something premade to build off of, consider getting something like a covered dog kennel and then reinforce it with hardware cloth at least the first few feet up from the bottom, and aproned out.  That should provide more security at a reasonable cost with minimal work.